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79 results on '"Dominique Chapelle"'

1. A biomechanics-based parametrized cardiac end-diastolic pressure–volume relationship for accurate patient-specific calibration and estimation

Author: Dominique Chapelle and Arthur Le Gall
Subjects: Medicine, Science
Abstract: Abstract A simple power law has been proposed in the pioneering work of Klotz et al. (Am J Physiol Heart Circ Physiol 291(1):H403–H412, 2006) to approximate the end-diastolic pressure–volume relationship of the left cardiac ventricle, with limited inter-individual variability provided the volume is adequately normalized. Nevertheless, we use here a biomechanical model to investigate the sources of the remaining data dispersion observed in the normalized space, and we show that variations of the parameters of the biomechanical model realistically account for a substantial part of this dispersion. We therefore propose an alternative law based on the biomechanical model that embeds some intrinsic physical parameters, which directly enables personalization capabilities, and paves the way for related estimation approaches.
Published: 2023
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2. Dimensional reduction of a poromechanical cardiac model for myocardial perfusion studies

Author: Radomír Chabiniok, Bruno Burtschell, Dominique Chapelle, and Philippe Moireau
Subjects: Poroelasticity, Biomechanical modeling, Computational physiology, Myocardial perfusion, Ischemic heart disease, Microvascular disease, Engineering (General). Civil engineering (General), TA1-2040
Abstract: In this paper, we adapt a previously developed poromechanical formulation to model the perfusion of myocardium during a cardiac cycle. First, a complete model is derived in 3D. Then, we perform a dimensional reduction under the assumption of spherical symmetry and propose a numerical algorithm that enables us to perform simulations of the myocardial perfusion throughout the cardiac cycle. These simulations illustrate the use of the proposed model to represent various physiological and pathological scenarios, specifically the vasodilation in the coronary network (to reproduce the standard clinical assessment of myocardial perfusion and perfusion reserve), the stenosis of a large coronary artery, an increased vascular resistance in the microcirculation (microvascular disease) and the consequences of inotropic activation (increased myocardial contractility) particularly at the level of the systolic flow impediment. Our results show that the model gives promising qualitative reproductions of complex physiological phenomena. This paves the way for future quantitative studies using clinical or experimental data.
Published: 2022
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3. Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics

Author: Alexandre Imperiale, Dominique Chapelle, and Philippe Moireau
Subjects: Data assimilation, Estimation, Cardiac modeling, Tagged-MRI, Patient-specific model, Mechanics of engineering. Applied mechanics, TA349-359, Systems engineering, TA168
Abstract: Abstract Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.
Published: 2021
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4. Thermodynamic properties of muscle contraction models and associated discrete-time principles

Author: François Kimmig, Dominique Chapelle, and Philippe Moireau
Subjects: Muscle contraction, Sliding filaments, Thermodynamically consistent time-discretization, Clausius–Duhem inequality, Mechanics of engineering. Applied mechanics, TA349-359, Systems engineering, TA168
Abstract: Abstract Considering a large class of muscle contraction models accounting for actin–myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermodynamic balances. Moreover, we propose a complete discretization strategy for which we are also able to obtain discrete versions of the thermodynamic balances and other properties. Our major objective is to show how the thermodynamics of such models can be tracked after discretization, including when they are coupled to a macroscopic muscle formulation in the realm of continuum mechanics. Our approach allows to carefully identify the sources of energy and entropy in the system, and to follow them up to the numerical applications.
Published: 2019
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5. Dobutamine stress testing in patients with Fontan circulation augmented by biomechanical modeling.

Author: Bram Ruijsink, Konrad Zugaj, James Wong, Kuberan Pushparajah, Tarique Hussain, Philippe Moireau, Reza Razavi, Dominique Chapelle, and Radomír Chabiniok
Subjects: Medicine, Science
Abstract: Understanding (patho)physiological phenomena and mechanisms of failure in patients with Fontan circulation-a surgically established circulation for patients born with a functionally single ventricle-remains challenging due to the complex hemodynamics and high inter-patient variations in anatomy and function. In this work, we present a biomechanical model of the heart and circulation to augment the diagnostic evaluation of Fontan patients with early-stage heart failure. The proposed framework employs a reduced-order model of heart coupled with a simplified circulation including venous return, creating a closed-loop system. We deploy this framework to augment the information from data obtained during combined cardiac catheterization and magnetic resonance exams (XMR), performed at rest and during dobutamine stress in 9 children with Fontan circulation and 2 biventricular controls. We demonstrate that our modeling framework enables patient-specific investigation of myocardial stiffness, contractility at rest, contractile reserve during stress and changes in vascular resistance. Hereby, the model allows to identify key factors underlying the pathophysiological response to stress in these patients. In addition, the rapid personalization of the model to patient data and fast simulation of cardiac cycles make our framework directly applicable in a clinical workflow. We conclude that the proposed modeling framework is a valuable addition to the current clinical diagnostic XMR exam that helps to explain patient-specific stress hemodynamics and can identify potential mechanisms of failure in patients with Fontan circulation.
Published: 2020
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6. Monitoring of cardiovascular physiology augmented by a patient-specific biomechanical model during general anesthesia. A proof of concept study.

Author: Arthur Le Gall, Fabrice Vallée, Kuberan Pushparajah, Tarique Hussain, Alexandre Mebazaa, Dominique Chapelle, Étienne Gayat, and Radomír Chabiniok
Subjects: Medicine, Science
Abstract: During general anesthesia (GA), direct analysis of arterial pressure or aortic flow waveforms may be inconclusive in complex situations. Patient-specific biomechanical models, based on data obtained during GA and capable to perform fast simulations of cardiac cycles, have the potential to augment hemodynamic monitoring. Such models allow to simulate Pressure-Volume (PV) loops and estimate functional indicators of cardiovascular (CV) system, e.g. ventricular-arterial coupling (Vva), cardiac efficiency (CE) or myocardial contractility, evolving throughout GA. In this prospective observational study, we created patient-specific biomechanical models of heart and vasculature of a reduced geometric complexity for n = 45 patients undergoing GA, while using transthoracic echocardiography and aortic pressure and flow signals acquired in the beginning of GA (baseline condition). If intraoperative hypotension (IOH) appeared, diluted norepinephrine (NOR) was administered and the model readjusted according to the measured aortic pressure and flow signals. Such patients were a posteriori assigned into a so-called hypotensive group. The accuracy of simulated mean aortic pressure (MAP) and stroke volume (SV) at baseline were in accordance with the guidelines for the validation of new devices or reference measurement methods in all patients. After NOR administration in the hypotensive group, the percentage of concordance with 10% exclusion zone between measurement and simulation was >95% for both MAP and SV. The modeling results showed a decreased Vva (0.64±0.37 vs 0.88±0.43; p = 0.039) and an increased CE (0.8±0.1 vs 0.73±0.11; p = 0.042) in hypotensive vs normotensive patients. Furthermore, Vva increased by 92±101%, CE decreased by 13±11% (p < 0.001 for both) and contractility increased by 14±11% (p = 0.002) in the hypotensive group post-NOR administration. In this work we demonstrated the application of fast-running patient-specific biophysical models to estimate PV loops and functional indicators of CV system using clinical data available during GA. The work paves the way for model-augmented hemodynamic monitoring at operating theatres or intensive care units to enhance the information on patient-specific physiology.
Published: 2020
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7. Prediction of Ventricular Mechanics After Pulmonary Valve Replacement in Tetralogy of Fallot by Biomechanical Modeling: A Step Towards Precision Healthcare

Author: Camille Hancock Friesen, Gerald F. Greil, Radomir Chabiniok, Maria Gusseva, Dominique Chapelle, Tarique Hussain, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], University of Nebraska Medical Center, University of Nebraska System, Czech Technical University in Prague (CTU), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: medicine.medical_specialty, medicine.medical_treatment, 0206 medical engineering, Biomedical Engineering, 02 engineering and technology, 030204 cardiovascular system & hematology, Contractility, 03 medical and health sciences, 0302 clinical medicine, Afterload, Valve replacement, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Internal medicine, Pulmonary Valve Replacement, Medicine, ComputingMilieux_MISCELLANEOUS, Ventricular mechanics, Tetralogy of Fallot, business.industry, valvular heart disease, medicine.disease, 020601 biomedical engineering, 3. Good health, medicine.anatomical_structure, Ventricle, Cardiology, [SDV.IB]Life Sciences [q-bio]/Bioengineering, business, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology
Abstract: Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient’s pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSMpre, and patient-specific models of the same patients created post-PVR (PSMpost)—both created in our previous published work. Using the PSMpre and assuming cessation of the pulmonary regurgitation and a progressive decrease of RVOT resistance, we built relationships between the contractility and RVOT resistance post-PVR. The predictive value of such in silico obtained relationships were tested against the PSMpost, i.e. the models created from the actual post-PVR datasets. Our results show a linear 1-dimensional relationship between the in silico predicted contractility post-PVR and the RVOT resistance. The predicted contractility was close to the contractility in the PSMpost model with a mean (± SD) difference of 6.5 (± 3.0)%. The relationships between the contractility predicted by in silico PVR vs. RVOT resistance have a potential to inform clinicians about hypothetical mechanical response of the ventricle based on the degree of pre-operative RVOTO.
Published: 2021
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8. Biomechanical Modeling to Inform Pulmonary Valve Replacement in Tetralogy of Fallot Patients after Complete Repair

Author: Gerald F. Greil, Radomir Chabiniok, Keren Hasbani, Dominique Chapelle, Camille L. Hancock Friesen, Maria Gusseva, Animesh Tandon, Cécile Patte, Philippe Moireau, Tarique Hussain, Martin Genet, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], University of Texas at Austin [Austin], Czech Technical University in Prague (CTU), King‘s College London, Guy's and St Thomas' Hospital [London], École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Adult, Male, Reoperation, medicine.medical_specialty, Percutaneous, Heart Ventricles, 0206 medical engineering, Magnetic Resonance Imaging, Cine, 02 engineering and technology, 030204 cardiovascular system & hematology, Models, Biological, Article, Contractility, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Cardiovascular modeling, Pulmonary Valve Replacement, Internal medicine, medicine.artery, Humans, Medicine, Abnormalities, Multiple, Cardiac Surgical Procedures, Retrospective Studies, Tetralogy of Fallot, Heart Valve Prosthesis Implantation, Cardiovascular magnetic resonance imaging, Pulmonary Valve, medicine.diagnostic_test, business.industry, Hemodynamics, Magnetic resonance imaging, Retrospective cohort study, Translational research, medicine.disease, 020601 biomedical engineering, Personalized medicine, Pulmonary Valve Insufficiency, Pulmonary artery, Cardiology, Female, Biomechanical model, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Myocardial contractility, Cardiology and Cardiovascular Medicine, business, Follow-Up Studies
Abstract: BACKGROUND: A biomechanical model of the heart can be used to incorporate multiple data sources (electrocardiography, imaging, invasive hemodynamics). The purpose of this study was to use this approach in a cohort of patients with tetralogy of Fallot after complete repair (rTOF) to assess comparative influences of residual right ventricular outflow tract obstruction (RVOTO) and pulmonary regurgitation on ventricular health. METHODS: Twenty patients with rTOF who underwent percutaneous pulmonary valve replacement (PVR) and cardiovascular magnetic resonance imaging were included in this retrospective study. RESULTS: RV contractility before PVR (mean 66 ± kPa, mean ± standard deviation) was increased in patients with rTOF compared with normal RV (38–48 kPa) (P < 0.05). The contractility decreased significantly in all patients after PVR (P < 0.05). Patients with predominantly RVOTO demonstrated greater reduction in contractility (median decrease 35%) after PVR than those with predominant pulmonary regurgitation (median decrease 11%). The model simulated post-PVR decreased EDV for the majority and suggested an increase of Q(eff)—both in line with published data. CONCLUSIONS: This study used a biomechanical model to synthesize multiple clinical inputs and give an insight into RV health. Individualized modeling allows us to predict the RV response to PVR. Initial data suggest that residual RVOTO imposes greater ventricular work than isolated pulmonary regurgitation. Biomechanical models specific to individual patient and physiology (before and after PVR) were created and used to estimate the RV myocardial contractility. The ability of models to capture post-PVR changes of right ventricular (RV) end-diastolic volume (EDV) and effective flow in the pulmonary artery (Qeff) was also compared with expected values.
Published: 2021
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9. Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes

Author: Dominique Chapelle, Philippe Moireau, François Kimmig, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Computer science, Computational Mechanics, Ocean Engineering, Context (language use), multi-scale modeling, Sarcomere, biomechanics, 03 medical and health sciences, Myosin head, 0302 clinical medicine, numerical methods, 030304 developmental biology, 0303 health sciences, Frank–Starling law of the heart, Hierarchical modeling, Applied Mathematics, Mechanical Engineering, Numerical analysis, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Multiscale modeling, multiscale modeling, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computational Mathematics, Computational Theory and Mathematics, Coupling (computer programming), Frank-Starling mechanism, sarcomere, Biological system, 030217 neurology & neurosurgery, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; In the context of cardiac muscle modeling, the availability of the myosin heads in the sarcomeres varies over the heart cycle contributing to the Frank-Starling mechanism at the organ level. In this paper, we propose a new approach that allows to extend the Huxley'57 muscle contraction model equations to incorporate this variation. This extension is built in a thermodynamically consistent manner, and we also propose adapted numerical methods that satisfy thermodynamical balances at the discrete level. Moreover, this whole approach-both for the model and the numerics-is devised within a hierarchical strategy enabling the coupling of the microscopic sarcomere-level equations with the macroscopic tissue-level description. As an important illustration, coupling our model with a previously proposed simplified heart model, we demonstrate the ability of the modeling and numerical framework to capture the essential features of the Frank-Starling mechanism.
Published: 2021
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10. Model-Assisted Time-Synchronization of Cardiac MR Image and Catheter Pressure Data

Author: Mohamed Abdelghafar Hussein, Maria Gusseva, Radomir Chabiniok, Surendranath R. Veeram Reddy, Gerald F. Greil, Daniel A. Castellanos, Joshua S. Greer, Tarique Hussain, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], Boston Children's Hospital, Pediatric department, Kafrelsheikh University, Kafrelsheikh University, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Faculty of Medicine, Kafrelsheikh University, Kafrelsheikh, Egypt
Subjects: Physics, cardiovascular modeling, time-synchronization of clinical data, medicine.diagnostic_test, Cardiac cycle, pressure volume loops, Image (category theory), Magnetic resonance imaging, personalized medicine, 030204 cardiovascular system & hematology, Type (model theory), 030218 nuclear medicine & medical imaging, 03 medical and health sciences, QRS complex, 0302 clinical medicine, Nuclear magnetic resonance, translational research, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Norm (mathematics), Ventricular pressure, medicine, [SDV.IB]Life Sciences [q-bio]/Bioengineering, interventional cardiovascular magnetic resonance imaging, Volume (compression)
Abstract: International audience; When combining cardiovascular magnetic resonance imaging (CMR) with pressure catheter measurements, the acquired imageand pressure data need to be synchronized in time. The time offset between the image and pressure data depends on a number of factors,such as the type and settings of the MR sequence, duration and shape of QRS complex or the type of catheter, and cannot be typically estimated beforehand. In the present work we propose using a biophysical heart model to synchronize the left ventricular (LV) pressure and volume (P-V) data. Ten patients, who underwent CMR and LV catheterization, were included. A biophysical model of reduced geometrical complexity with physiologically substantiated timing of each phase of the cardiac cycle was first adjusted to individual patients using basic morphological and functional indicators. The pressure and volume waveforms simulated by the patient-specific models were then used as templates to detect the time offset between the acquired ventricular pressure and volume waveforms. Time-varying ventricular elastance was derived from clinical data both as originally acquired as well as when time-synchronized, and normalized with respect to end-systolic time and maximum elastance value$E^N_\text {orig}(t)$, $E^N_\text {t-syn}(t)$, respectively). $E^N_\text {t-syn}(t)$ was significantly closer to the experimentally obtained $E^N_\text {exp}(t)$ published in the literature (p < 0.05, $L^2$ norm). The work concludes that the model-driven time-synchronization of P-V data obtained by catheter measurement and CMR allows to generate high quality P-V loops, which can then be used for clinical interpretation.
Published: 2021
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11. Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics

Author: Philippe Moireau, Dominique Chapelle, Alexandre Imperiale, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Département Imagerie et Simulation pour le Contrôle (DISC), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Laboratoire d'Intégration des Systèmes et des Technologies (LIST)
Subjects: Computer science, 0206 medical engineering, Image processing, 02 engineering and technology, Data type, Synthetic data, 030218 nuclear medicine & medical imaging, lcsh:TA168, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Medical imaging, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Engineering (miscellaneous), Flexibility (engineering), Measure (data warehouse), Tagged-MRI, business.industry, Applied Mathematics, Pattern recognition, Cardiac modeling, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, lcsh:Systems engineering, Modeling and Simulation, Patient-specific model, Artificial intelligence, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Focus (optics), business, lcsh:Mechanics of engineering. Applied mechanics, lcsh:TA349-359, Estimation
Abstract: Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.
Published: 2021
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12. A quasi-static poromechanical model of the lungs

Author: Cécile Patte, Martin Genet, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-10-EQPX-0037,MATMECA,MATériaux-MECAnique/Elaboration-Caractérisation-Observation-Modélisation-Simulation(2010), ANR-19-CE45-0007,LungManyScale,Biomécanique Computationnelle Pulmonaire: Modélisation Multi-échelle et Estimation(2019), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Mechanical Engineering, Respiration, 0206 medical engineering, Diaphragm, Poromechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 02 engineering and technology, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, Inverse Poromechanics, Modeling and Simulation, Finite Element Method, Pulmonary Mechanics, [SDV.MHEP.AHA]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO], Lung, Biotechnology
Abstract: International audience; The lung vital function of providing oxygen to the body heavily relies on its mechanical behavior, and the interaction with its complex environment. In particular, the large compliance and the porosity of the pulmonary tissue are critical for lung inflation and air inhalation, and the diaphragm, the pleura, the rib cage and intercostal muscles all play a role in delivering and controlling the breathing driving forces. In this paper, we introduce a novel poromechanical model of the lungs. The constitutive law is derived within a general poromechanics theory via the formulation of lung-specific assumptions, leading to a hyperelastic potential reproducing the volume response of the pulmonary mixture to a change of pressure. Moreover, physiological boundary conditions are formulated to account for the interaction of the lungs with their surroundings, including a following pressure and bilateral frictionless contact. A strategy is established to estimate the unloaded configuration from a given loaded state, with a particular focus on ensuring a positive porosity. Finally, we illustrate through several realistic examples the relevance of our model and its potential clinical applications.
Published: 2021
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13. Combining data assimilation and machine learning to build data-driven models for unknown long time dynamics—Applications in cardiovascular modeling

Author: Francesco Regazzoni, Philippe Moireau, Dominique Chapelle, Modeling and Scientific Computing [Milano] (MOX), Politecnico di Milano [Milan] (POLIMI), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: cardiovascular modeling, Computer science, Differential equation, data‐driven modeling, 0206 medical engineering, Biomedical Engineering, Context (language use), 02 engineering and technology, 030204 cardiovascular system & hematology, Machine learning, computer.software_genre, Field (computer science), Data-driven, 03 medical and health sciences, 0302 clinical medicine, multiscale problems, Molecular Biology, data assimilation, Interpretability, Parametric statistics, Research Article ‐ Fundamental, Artificial neural network, business.industry, Applied Mathematics, Models, Theoretical, 020601 biomedical engineering, Test case, machine learning, Computational Theory and Mathematics, data-driven modeling, Modeling and Simulation, Artificial intelligence, business, computer, artificial neural networks, Algorithms, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Software
Abstract: We propose a method to discover differential equations describing the long‐term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast‐scale. Our methodology is based on a synergetic combination of data assimilation (DA), used to estimate the parameters associated with the known fast‐scale dynamics, and machine learning (ML), used to infer the laws underlying the slow‐scale dynamics. Specifically, by exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden. Then, we propose a ML algorithm that learns a parametric mathematical model from a collection of time series coming from the phenomenon to be modeled. Moreover, we study the interpretability of the data‐driven models obtained within the black‐box learning framework proposed in this paper. In particular, we show that every model can be rewritten in infinitely many different equivalent ways, thus making intrinsically ill‐posed the problem of learning a parametric differential equation starting from time series. Hence, we propose a strategy that allows to select a unique representative model in each equivalence class, thus enhancing the interpretability of the results. We demonstrate the effectiveness and noise‐robustness of the proposed methods through several test cases, in which we reconstruct several differential models starting from time series generated through the models themselves. Finally, we show the results obtained for a test case in the cardiovascular modeling context, which sheds light on a promising field of application of the proposed methods., We propose a method to discover differential equations describing the long‐term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast‐scale. Our methodology is based on a synergetic combination of data assimilation, used to estimate the parameters associated with the known fast‐scale dynamics, and machine learning, used to infer the laws underlying the slow‐scale dynamics. By exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden.
Published: 2021
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14. Personalized pulmonary poromechanics

Author: Pierre-Yves Brillet, Dominique Chapelle, Catalin Fetita, Cécile Patte, Martin Genet, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Paris (IP Paris), Département Advanced Research And Techniques For Multidimensional Imaging Systems (TSP - ARTEMIS), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), ARMEDIA (ARMEDIA-SAMOVAR), Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP)-Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Hypoxie et Poumon : pneumopathologies fibrosantes, modulations ventilatoires et circulatoires (H&P), UFR SMBH-Université Sorbonne Paris Nord, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Département Advanced Research And Techniques For Multidimensional Imaging Systems (ARTEMIS)
Subjects: Computer science, 0206 medical engineering, Poromechanics, Biomedical Engineering, Bioengineering, 02 engineering and technology, [SDV.MHEP.PSR]Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract, 03 medical and health sciences, 0302 clinical medicine, Pulmonary mechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Control engineering, 030229 sport sciences, General Medicine, respiratory system, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 3. Good health, Computer Science Applications, Human-Computer Interaction, Current (fluid), Estimation, Simulation
Abstract: International audience; Lung biomechanics has been extensively studied by physiologists, experimentally as well as theoretically, laying the ground for our current fundamental understanding of the relationship between function and mechanical behavior. However, many questions remain, notably in the intricate coupling between the multiple constituents. These fundamental questions represent real clinical challenges, as pulmonary diseases are an important health burden. Interstitial lung diseases, for instance, affect several million people globally. Idiopathic Pulmonary Fibrosis (IPF), notably, a progressive form of interstitial lung diseases where some alveolar septa get thicker and stiffer while others get completely damaged, remains poorly understood, poorly diagnosed, and poorly treated (Nunes et al. 2015).
Published: 2020
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15. Stochastic modeling of chemical–mechanical coupling in striated muscles

Author: Dominique Chapelle, Philippe Moireau, Matthieu Caruel, Laboratoire de Modélisation et Simulation Multi Echelle (MSME), Université Paris-Est Marne-la-Vallée (UPEM)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Université Paris-Est Marne-la-Vallée (UPEM), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Mechanical Phenomena, power stroke, 0206 medical engineering, Probability density function, 02 engineering and technology, Myosins, Models, Biological, Sarcomere, Myosin head, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Isometric Contraction, [SDV.MHEP.PHY]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO], muscle modeling, sliding filament, Statistical physics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Power stroke, Physics, Coupling, Stochastic Processes, Partial differential equation, Viscosity, Mechanical Engineering, 020601 biomedical engineering, Muscle, Striated, Biomechanical Phenomena, Macroscopic scale, Modeling and Simulation, Calibration, Thermodynamics, cross-bridge, sarcomere, Langevin equations, Fokker-Planck equations, Biotechnology
Abstract: International audience; We propose a chemical-mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs) - one of which associated with the so-called power stroke - and two possible chemical states, i.e. bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical-mechanical model, and (2) to thus account - at the macroscopic scale - for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker-Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics, and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight, and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data - taken here for skeletal muscles - and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models.
Published: 2019
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16. Cardiac displacement tracking with data assimilation combining a biomechanical model and an automatic contour detection

Author: Gautier Bureau, Dominique Chapelle, Jürgen Weese, Jaroslav Tintera, Radomir Chabiniok, Alexandra Groth, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), King‘s College London, Philips Research [Germany], Philips Research, Institute for Clinical and Experimental Medicine (IKEM), Zemzemi, Nejib, Ozenne, Valéry, Vigmond, Edward, Coudière, Yves, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Computational model, Computer science, business.industry, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, 02 engineering and technology, Tracking (particle physics), 020601 biomedical engineering, Biophysical heart modeling, cine MRI, Displacement (vector), Bottleneck, 030218 nuclear medicine & medical imaging, Term (time), Cine mri, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Computer vision, Artificial intelligence, business, [SDV.IB.BIO]Life Sciences [q-bio]/Bioengineering/Biomaterials, Cardiac imaging
Abstract: International audience; Data assimilation in computational models represents an essential step in building patient-specific simulations. This work aims at circumventing one major bottleneck in the practical use of data assimilation strategies in cardiac applications, namely, the difficulty of formulating and effectively computing adequate data-fitting term for cardiac imaging such as cine MRI. We here provide a proof-of-concept study of data assimilation based on automatic contour detection. The tissue motion simulated by the data assimilation framework is then assessed with displacements extracted from tagged MRI in six subjects, and the results illustrate the performance of the proposed method, including for circumferential displacements, which are not well extracted from cine MRI alone.
Published: 2019
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17. Minimally-invasive estimation of patient-specific end-systolic elastance using a biomechanical heart model

Author: Radomir Chabiniok, Dominique Chapelle, Fabrice Vallée, Arthur Le Gall, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X), Service d'Anesthésie-Réanimation [AP-HP Hôpitaux Saint-Louis Lariboisière], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Lariboisière-Fernand-Widal [APHP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), School of Biomedical Engineering & Imaging Sciences [London], Guy's and St Thomas' Hospital [London]-King‘s College London, ANAESTASSIST, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), King‘s College London-Guy's and St Thomas' Hospital [London], Coudière, Yves, Ozenne, Valéry, Vigmond, Edward, Zemzemi, Nejib, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS), Assistance publique - Hôpitaux de Paris (AP-HP) (APHP)-Hôpital Lariboisière-Université Paris Diderot - Paris 7 (UPD7), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Time-varying elastance, Linear function (calculus), [SDV]Life Sciences [q-bio], 0206 medical engineering, Patient-specific biophysical modelling, 02 engineering and technology, State (functional analysis), Function (mathematics), 030204 cardiovascular system & hematology, Patient specific, 020601 biomedical engineering, Confidence interval, [SHS]Humanities and Social Sciences, Combinatorics, 03 medical and health sciences, 0302 clinical medicine, End systolic elastance, Time-varying elastan, End-systolic elastance estimation, Sensitivity (control systems), Uniqueness, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology, Mathematics
Abstract: The end-systolic elastance ($E_{\text {es}}$) – the slope of the end-systolic pressure-volume relationship (ESPVR) at the end of ejection phase – has become a reliable indicator of myocardial functional state. The estimation of $E_{\text {es}}$ by the original multiple-beat method is invasive, which limits its routine usage. By contrast, non-invasive single-beat estimation methods, based on the assumption of the linearity of ESPVR and the uniqueness of the normalised time-varying elastance curve $E^N(t)$ across subjects and physiology states, have been applied in a number of clinical studies. It is however known that these two assumptions have a limited validity, as ESPVR can be approximated by a linear function only locally, and $E^N(t)$ obtained from a multi-subject experiment includes a confidence interval around the mean function. Using datasets of 3 patients undergoing general anaesthesia (each containing aortic flow and pressure measurements at baseline and after introducing a vasopressor noradrenaline), we first study the sensitivity of two single-beat methods—by Sensaki et al. and by Chen et al.—to the uncertainty of $E^N(t)$. Then, we propose a minimally-invasive method based on a patient-specific biophysical modelling to estimate the whole time-varying elastance curve $E^{\text {model}}(t)$. We compare $E^{\text {model}}_{\text {es}}$ with the two single-beat estimation methods, and the normalised varying elastance curve $E^{N,\text {model}}(t)$ with $E^{N}(t)$ from published physiological experiments.
Published: 2019
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18. Numerical analysis for an energy-stable total discretization of a poromechanics model with inf-sup stability

Author: Philippe Moireau, Dominique Chapelle, Bruno Burtschell, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Spacetime, Discretization, energy estimates, Applied Mathematics, Numerical analysis, Poromechanics, poromechanics, 010103 numerical & computational mathematics, incompressibility, 01 natural sciences, Stability (probability), 010101 applied mathematics, inf-sup, Nonlinear system, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], Compressibility, Applied mathematics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, total discretization, Energy (signal processing), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; We consider a previously proposed general nonlinear poromechanical formulation, and we derive a linearized version of this model. For this linearized model, we obtain an existence result and we propose a complete discretization strategy - in time and space - with a special concern for issues associated with incompressible or nearly-incompressible behavior. We provide a detailed mathematical analysis of this strategy, the main result being an error estimate uniform with respect to the compressibility parameter. We then illustrate our approach with detailed simulation results and we numerically investigate the importance of the assumptions made in the analysis, including the fulfillment of specific inf-sup conditions.
Published: 2019
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19. Apprehending the effects of mechanical deformations in cardiac electrophysiology - An homogenization approach

Author: Jean-Frédéric Gerbeau, Annabelle Collin, Philippe Moireau, Dominique Chapelle, Sébastien Imperiale, Institut Polytechnique de Bordeaux (Bordeaux INP), Modélisation Mathématique pour l'Oncologie (MONC), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Inria Siège, Institut National de Recherche en Informatique et en Automatique (Inria), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Physics, Cell specific, 0303 health sciences, Cardiac electrophysiology, Applied Mathematics, Multiphysics, 0206 medical engineering, Microscopic level, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 02 engineering and technology, 020601 biomedical engineering, Homogenization (chemistry), 03 medical and health sciences, Classical mechanics, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Modeling and Simulation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 030304 developmental biology
Abstract: International audience; We follow a formal homogenization approach to investigate the effects of mechanical deformations in electrophysiology models relying on a bidomain description of ionic motion at the microscopic level. To that purpose, we extend these microscopic equations to take into account the mechanical deformations, and proceed by recasting the problem in the framework of classical two-scale homogenization in periodic media, and identifying the equations satisfied by the first coefficients in the formal expansions. The homogenized equations reveal some interesting effects related to the microstructure - and associated with a specific cell problem to be solved to obtain the macroscopic conductivity tensors - in which mechanical deformations play a non-trivial role, i.e. do not simply lead to a standard bidomain problem posed in the deformed configuration. We then present detailed numerical illustrations of the homogenized model with coupled cardiac electrical-mechanical simulations - all the way to ECG simulations - albeit without taking into account the abundantly-investigated effect of mechanical deformations in ionic models, in order to focus here on other effects. And in fact our numerical results indicate that these other effects are numerically of a comparable order, and therefore cannot be disregarded.
Published: 2019
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20. Thermodynamic properties of muscle contraction models and associated discrete-time principles

Author: Dominique Chapelle, Philippe Moireau, François Kimmig, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Large class, 74F25 ·74H15 · 65M12 ·35Q79 and 92C45, Discretization, 02 engineering and technology, Clausius–Duhem inequality, 01 natural sciences, lcsh:TA168, muscle contraction, 0203 mechanical engineering, medicine, Computational Science and Engineering, Statistical physics, 0101 mathematics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Engineering (miscellaneous), thermodynamically consistent time-discretization, Mathematics, Clausius-Duhem inequality, Continuum mechanics, Applied Mathematics, sliding filaments, Computer Science Applications, 010101 applied mathematics, 020303 mechanical engineering & transports, Discrete time and continuous time, lcsh:Systems engineering, Modeling and Simulation, medicine.symptom, lcsh:Mechanics of engineering. Applied mechanics, lcsh:TA349-359, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Muscle contraction
Abstract: International audience; Considering a large class of muscle contraction models accounting for actin-myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermodynamic balances. Moreover, we propose a complete discretization strategy for which we are also able to obtain discrete versions of the thermodynamic balances and other properties. Our major objective is to show how the thermodynamics of such models can be tracked after discretization, including when they are coupled to a macroscopic muscle formulation in the realm of continuum mechanics. Our approach allows to carefully identify the sources of energy and entropy in the system, and to follow them up to the numerical applications.
Published: 2019
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21. Airborne ultrasound surface motion camera: application to seismocardiography

Author: Pavel Shirkovskiy, R.K. Ing, Dominique Chapelle, Mathias Fink, Nathan Jeger-Madiot, Alexandre Laurin, Institut Langevin - Ondes et Images (UMR7587) (IL), Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Synthetic aperture radar, Physics and Astronomy (miscellaneous), Computer science, Wave propagation, Acoustics, non-contact seismocardiography, 030204 cardiovascular system & hematology, Accelerometer, 01 natural sciences, cardiac mechanics, 03 medical and health sciences, Acceleration, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Position (vector), [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Center frequency, surface motion, business.industry, 010401 analytical chemistry, Ultrasound, airborne ultrasound vibrometry, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], cardio-vascular signals, Non-contact ultrasonic imaging, 0104 chemical sciences, Identifiability, business
Abstract: International audience; The recent achievements in the accelerometer-based seismocardiography field indicate a strong potential for this technique to address wide variety of clinical needs. Recordings from different locations on the chest can give a more comprehensive observation and interpretation of wave propagation phenomena than a single-point recording, can validate existing modeling assumptions (such as the representation of the sternum as a single solid body), and provide better identifiability for models using richer recordings. Ultimately, the goal is to advance our physiological understanding of the processes to provide useful data to promote cardiovascular health. Accelerometer-based multichannel system is a contact method and laborious for use in practice, also even ultralight accelerometers can cause non-negligible loading effects. We propose a new contactless ultrasound imaging method to measure thoracic and abdominal surface motions, demonstrating that it is adequate for typical seismocardiogram use. The developed method extends non-contact surface-vibrometry to fast 2D mapping by originally combining multi-element airborne ultrasound arrays, a synthetic aperture implementation and pulsed-waves. Experimental results show the ability of the developed method to obtain 2D seismocardiographic maps of the body surface 30×40 cm 2 in dimension, with a temporal sampling rate of several hundred Hz, using ultrasound waves with the central frequency of 40 kHz. Our implementation was validated in-vivo on eight healthy human participants. The shape and position of the zone of maximal absolute acceleration and velocity during the cardiac cycle were also observed. This technology could potentially be used to obtain more complete cardio-vascular information than single-source SCG in and out of clinical environments, due to enhanced identifiability provided by distributed measurements, and observation of propagation phenomena.
Published: 2018
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22. Contactless Mapping of Thoracic and Abdominal Movements: Applications for Seismocardiography

Author: Dominique Chapelle, R.K. Ing, Alexandre Laurin, Mathias Fink, and Pavel Shirkovskiy
Subjects: Thorax, Computer science, 010401 analytical chemistry, 0206 medical engineering, Measure (physics), 02 engineering and technology, Accelerometer, Frame rate, 020601 biomedical engineering, 01 natural sciences, Motion (physics), 0104 chemical sciences, Ultrasonic imaging, medicine.anatomical_structure, medicine, Abdomen, Ultrasonic sensor, Biomedical engineering
Abstract: Seismocardiography has been well studied in terms of analysis, applications, and methods of measurement. However, there remains a lack of research into the explanation and modelling of the involved phenomena. We propose a new contactless method to measure thoracic and sternal movements, demonstrate that it is adequate for typical seismocardiogram use. An ultrasonic diagnostic tool called ICARE (CArdio REspiratory Imager) was designed to perform non-contact ultrasonic waves imaging on the thorax and abdomen. In addition to ICARE measurements an accelerometer was placed above the xiphoid of 3 participants (male, age 39±11). Both ICARE and accelerometer measurements were performed concurrently. Experimental results show the ability of the ICARE system to obtain 3D seismocardiographic images with high frequency frame rate. Furthermore, this technology could potentially be used to obtain cardio-vascular information in and out of clinical environments, significantly lowering the required time and effort.
Published: 2017
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23. Effective and energy-preserving time discretization for a general nonlinear poromechanical formulation

Author: Dominique Chapelle, Bruno Burtschell, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)-Inria Saclay - Ile de France
Subjects: Coupling, Mathematical optimization, Work (thermodynamics), Discretization, Mechanical Engineering, 010103 numerical & computational mathematics, Dissipation, 01 natural sciences, Computer Science Applications, 010101 applied mathematics, Nonlinear system, Modeling and Simulation, Component (UML), Applied mathematics, General Materials Science, 0101 mathematics, Energy (signal processing), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Civil and Structural Engineering, Free energy principle, Mathematics
Abstract: Proposed time discretization scheme for general two-phase poromechanical model.Discrete energy estimate with the total free energy of the mixture, in a general nonlinear framework.Numerical examples with representative test problems. We consider a general nonlinear poromechanical model, formulated based on fundamental thermodynamics principle, suitable for representing the coupling of rapid internal fluid flows with large deformations of the solid, and compatible with a wide class of constitutive behavior. The objective of the present work is to propose for this model a time discretization scheme of the partitioned type, to allow the use of existing time schemes and possibly separate solvers for each component of the model, i.e. for the fluid and the solid. To that purpose, we adapt and extend an earlier proposed approach devised for fluid-structure interaction in an Arbitrary Lagrangian-Eulerian framework. We then establish an energy estimate for the resulting time scheme, in a form that is consistent with the underlying energy principle in the poromechanical formulation, up to some numerical dissipation effects and some perturbations that we have carefully identified and assessed. In addition, we provide some numerical illustrations of our numerical strategy with test problems that present typical features of large strains and rapid fluid flows, and also a case of singular transition related to total drainage. An example of challenging application envisioned for this model and associated numerical coupling scheme concerns the perfusion of the heart.
Published: 2017
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24. Assessment of Atrioventricular Valve Regurgitation Using Biomechanical Cardiac Modeling

Author: Christoph Kiesewetter, Reza Razavi, Dominique Chapelle, Tarique Hussain, Radomir Chabiniok, and Philippe Moireau
Subjects: medicine.medical_specialty, Atrioventricular valve, medicine.diagnostic_test, business.industry, 0206 medical engineering, Therapy planning, 02 engineering and technology, Regurgitation (circulation), Systolic function, 030204 cardiovascular system & hematology, 020601 biomedical engineering, Reduced order, 03 medical and health sciences, 0302 clinical medicine, medicine.anatomical_structure, Ventricle, Cardiac magnetic resonance imaging, Internal medicine, medicine, Cardiology, business
Abstract: In this work we introduce the modeling of atrioventricular valve regurgitation in a spatially reduced order biomechanical heart model. The model can be fast calibrated using non-invasive data of cardiac magnetic resonance imaging and provides an objective measure of contractile properties of the myocardium in the volume overloaded ventricle, for which the real systolic function may be masked by the significant level of the atrioventricular valve regurgitation. After demonstrating such diagnostic capabilities, we show the potential of modeling to address some clinical questions concerning possible therapeutic interventions for specific patients. The fast running of the model allows targeting specific questions of referring clinicians in a clinically acceptable time.
Published: 2017
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25. Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

Author: Radomir, Chabiniok, Vicky Y, Wang, Myrianthi, Hadjicharalambous, Liya, Asner, Jack, Lee, Maxime, Sermesant, Ellen, Kuhl, Alistair A, Young, Philippe, Moireau, Martyn P, Nash, Dominique, Chapelle, and David A, Nordsletten
Subjects: translational cardiac modelling, patient-specific modelling, heart mechanics, Review Article, data–model fusion, cardiac mechanics, Part II: Methodology Needed for Establishing a Clinically Relevant Human Physiome
Abstract: With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.
Published: 2016

26. ENERGY-PRESERVING MUSCLE TISSUE MODEL: FORMULATION AND COMPATIBLE DISCRETIZATIONS

Author: Philippe Moireau, Michel Sorine, Patrick Le Tallec, Dominique Chapelle, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), SIgnals and SYstems in PHysiology & Engineering (SISYPHE), and École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Muscle tissue, Engineering, Mathematical optimization, Discretization, Computer Networks and Communications, 0206 medical engineering, Computational Mechanics, Energy balance, 02 engineering and technology, muscle tissue modeling, Striated Muscles, 01 natural sciences, myocardium, medicine, time and space discretizations, 0101 mathematics, multi scale, Chemical activity, Oxygen supply, Spacetime, business.industry, energy balance, 020601 biomedical engineering, 010101 applied mathematics, medicine.anatomical_structure, Control and Systems Engineering, business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Energy (signal processing)
Abstract: International audience; In this paper we propose a muscle tissue model -- valid for striated muscles in general, and for the myocardium in particular -- based on a multi-scale physiological description. This model extends and refines an earlier-proposed formulation by allowing to account for all major energy exchanges and balances, from the chemical activity coupled with oxygen supply to the production of actual mechanical work, namely, the biological function of the tissue. We thus perform a thorough analysis of the energy mechanisms prevailing at the various scales, and we proceed to propose a complete discretization strategy -- in time and space -- respecting the same balance laws. This will be crucial in future works to adequately model the many important physiological -- normal and pathological -- phenomena associated with these energy considerations.
Published: 2012
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27. Myocardial transversely isotropic material parameter estimation from in-silico measurements based on a reduced-order unscented Kalman filter

Author: Jiahe Xi, Philippe Moireau, Pablo Lamata, Nic Smith, Jack Lee, Dominique Chapelle, Computing Laboratory (OUCL), University of Oxford [Oxford], Biomedical Engineering Department, King‘s College London, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and University of Oxford
Subjects: Models, Anatomic, Computer science, Heart Ventricles, Finite Element Analysis, 0206 medical engineering, Constitutive equation, Biomedical Engineering, 02 engineering and technology, Ventricular Function, Left, Displacement (vector), Biomaterials, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Control theory, Transverse isotropy, Mechanical Phenomena, Estimation theory, Kalman filter, 020601 biomedical engineering, Finite element method, Biomechanical Phenomena, Nonlinear system, Nonlinear Dynamics, Mechanics of Materials, Feasibility Studies, Algorithm, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], 030217 neurology & neurosurgery
Abstract: International audience; Parameter estimation from non-invasive measurements is a crucial step in patient-specific cardiac modeling. It also has the potential to provide sig- nificant assistance in the clinical diagnosis of cardiac diseases through the quantification of myocardial material heterogeneity. In this paper, we for- mulate a novel Reduced-order Unscented Kalman Filter (rUKF) applied to the left ventricular (LV) nonlinear mechanical model based on cubic-Hermite finite elements. Material parameters in the widely-employed transversely isotropic Guccione's constitutive law are successfully identified for both ho- mogeneous and heterogeneous cases. We conclude that the four parameters in Guccione's law can be uniquely and correctly determined in silico from noisy displacement measurements of material points located on the myocar- dial surfaces. The future application of this novel and effective approach to real clinical measurements is thus promising.
Published: 2011
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28. Erratum of article 'Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems'

Author: Philippe Moireau and Dominique Chapelle
Subjects: Computational Mathematics, Identification (information), Control and Optimization, Unscented kalman filtering, Control and Systems Engineering, Control theory, Calculus of variations, Mathematics, Reduced order
Published: 2011
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29. euHeart: personalized and integrated cardiac care using patient-specific cardiovascular modelling

Author: Walther H. W. Schulze, Jatin Relan, Dominique Chapelle, Matt McCormick, Helko Lehmann, Philipp Beerbaum, Maxime Sermesant, David Nordsletten, Jos A. E. Spaan, Alejandro F. Frangi, Israel Valverde, Peter Hunter, Reza Rezavi, Rod Hose, Nicholas Ayache, Juergen Weese, Cristina Staicu, Maria Siebes, Hervé Delingette, Oscar Camara, Nic Smith, Adelaide de Vecchi, Martin W. Krueger, Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, Computing Laboratory (OUCL), University of Oxford, Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), Universitat Pompeu Fabra [Barcelona] (UPF), Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Instituto de Salud Carlos III [Madrid] (ISC)-ministerio de ciencia e innovacion, Institució Catalana de Recerca i Estudis Avançats (ICREA), Institute of Simulation and Graphics [Magdeburg], Otto-von-Guericke-Universität Magdeburg = Otto-von-Guericke University [Magdeburg] (OVGU), Analysis and Simulation of Biomedical Images (ASCLEPIOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institute of Biomedical Engineering [Karlsruhe], Karlsruhe Institute of Technology (KIT), Department of Cardiovascular Science [Sheffield], University of Sheffield [Sheffield], Academic Medical Center - Academisch Medisch Centrum [Amsterdam] (AMC), University of Amsterdam [Amsterdam] (UvA), Auckland Bioengineering Institute, University of Auckland [Auckland], Philips Research Laboratories [Eindhoven], Philips Research [Nederlands], Philips Research, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Division of Imaging Sciences, King‘s College London, NIHR Biomedical Research Centre [London], Guy's and St Thomas' NHS Foundation Trust-King‘s College London, University of Oxford [Oxford], Otto-von-Guericke University [Magdeburg] (OVGU), ACS - Amsterdam Cardiovascular Sciences, Biomedical Engineering and Physics, and Other Research
Subjects: Cardiac function curve, medicine.medical_specialty, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, Population, Biomedical Engineering, Biophysics, Pump function, Bioengineering, 02 engineering and technology, Disease, 030204 cardiovascular system & hematology, Bioinformatics, Biochemistry, Biomaterials, 03 medical and health sciences, 0302 clinical medicine, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Medicine, Clinical imaging, education, Intensive care medicine, education.field_of_study, business.industry, Virtual Physiological Human, Articles, Patient specific, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 3. Good health, Lifetime risk, business, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Biotechnology
Abstract: International audience; The loss of cardiac pump function accounts for a significant increase in both mortality and morbidity in Western society, where there is currently a one in four lifetime risk, and costs associated with acute and long-term hospital treatments are accelerating. The significance of cardiac disease has motivated the application of state-of-the-art clinical imaging techniques and functional signal analysis to aid diagnosis and clinical planning. Measurements of cardiac function currently provide high-resolution datasets for characterizing cardiac patients. However, the clinical practice of using population-based metrics derived from separate image or signal-based datasets often indicates contradictory treatments plans owing to inter-individual variability in pathophysiology. To address this issue, the goal of our work, demonstrated in this study through four specific clinical applications, is to integrate multiple types of functional data into a consistent framework using multi-scale computational modelling.
Published: 2011
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30. Joint state and parameter estimation for distributed mechanical systems

Author: Dominique Chapelle, Patrick Le Tallec, Philippe Moireau, Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), and École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Engineering, Observer (quantum physics), 0206 medical engineering, Computational Mechanics, General Physics and Astronomy, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], 02 engineering and technology, 01 natural sciences, Control theory, Robustness (computer science), Convergence (routing), Biomechanics, 0101 mathematics, business.industry, Estimation theory, Mechanical Engineering, Estimator, [PHYS.MECA.MSMECA]Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph], 020601 biomedical engineering, Computer Science Applications, 010101 applied mathematics, Mechanical system, Mechanics of Materials, Feature (computer vision), Data assimilation, State (computer science), Filtering, business, Estimation
Abstract: We present a novel strategy to perform estimation for a dynamical mechanical system in standard operating conditions, namely, without ad hoc experimental testing. We adopt a sequential approach, and the joint state-parameter estimation procedure is based on a state estimator inspired from collocated feedback control. This type of state estimator is chosen due to its particular effectiveness and robustness, but the methodology proposed to adequately extend state estimation to joint state-parameter estimation is general, and - indeed -applicable with any other choice of state feedback observer. The convergence of the resulting joint estimator is mathematically established. In addition, we demonstrate its effectiveness with a biomechanical test problem defined to feature the same essential characteristics as a heart model, in which we identify localized contractility and stiffness parameters using measurements of a type that is available in medical imaging.
Published: 2008
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31. A Luenberger observer for reaction-diffusion models with front position data

Author: Dominique Chapelle, Annabelle Collin, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Modélisation Mathématique pour l'Oncologie (MONC), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, European Union’s Seventh Framework Programme for research, technological development and demonstration, under grant agreement #611823 (VP2HF Project), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux]
Subjects: Numerical Analysis, Physics and Astronomy (miscellaneous), Observer (quantum physics), Eikonal equation, Estimation theory, Applied Mathematics, Cardiac electrophysiology, Kalman filter, Reaction-diffusion model, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, Computational Mathematics, Nonlinear system, Image processing, Control theory, Front propagation, Modeling and Simulation, Data assimilation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], State observer, Asymptotic expansion, Alpha beta filter, Mathematics
Abstract: International audience; We propose a Luenberger observer for reaction-diffusion models with propagating front features, and for data associated with the location of the front over time. Such models are considered in various application fields, such as electrophysiology, wild-land fire propagation and tumor growth modeling. Drawing our inspiration from image processing methods, we start by proposing an observer for the eikonal-curvature equation that can be derived from the reaction-diffusion model by an asymptotic expansion. We then carry over this observer to the underlying reaction-diffusion equation by an "inverse asymptotic analysis", and we show that the associated correction in the dynamics has a stabilizing effect for the linearized estimation error. We also discuss the extension to joint state-parameter estimation by using the earlier-proposed ROUKF strategy. We then illustrate and assess our proposed observer method with test problems pertaining to electrophysiology modeling, including with a realistic model of cardiac atria. Our numerical trials show that state estimation is directly very effective with the proposed Luenberger observer, while specific strategies are needed to accurately perform parameter estimation – as is usual with Kalman filtering used in a nonlinear setting – and we demonstrate two such successful strategies.
Published: 2015
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32. Patient-Specific Biomechanical Modeling of Cardiac Amyloidosis – A Case Study

Author: Aziz Guellich, Radomir Chabiniok, Jean-François Deux, Dominique Chapelle, Thibaud Damy, Alessandro Felder, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, Unité fonctionnelle insuffisance cardiaque, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital Henri Mondor-Université Paris-Est (UPE), Institut Mondor de Recherche Biomédicale (IMRB), Institut National de la Santé et de la Recherche Médicale (INSERM)-IFR10-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), H. van Assen, P. Bovendeerd, T. Delhaas, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: amyloidosis, medicine.medical_specialty, Heartbeat, business.industry, Amyloidosis, heart failure, Patient specific, medicine.disease, Surgery, cardiac modeling, Physical medicine and rehabilitation, Cardiac amyloidosis, patient-specific, Heart failure, medicine, business, Passive stiffness, Venous return curve, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We present a patient-specific biomechanical modeling framework and an initial case study for investigating cardiac amyloidosis (CA). Our patient-specific heartbeat simulations are in good agreement with the data, and our model calibration indicates that the major effect of CA in the biophysical behavior lies in a dramatic increase of the passive stiffness. We also conducted a preliminary trial for predicting the effects of pharmacological treatments – which is an important clinical challenge – based on the model combined with a simple venous return representation. This requires further investigation and validation, albeit provides some valuable preliminary insight.
Published: 2015
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33. Sequential State Estimation for Electrophysiology Models with Front Level-Set Data Using Topological Gradient Derivations

Author: Annabelle Collin, Dominique Chapelle, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Modélisation Mathématique pour l'Oncologie (MONC), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, H. van Assen, P. Bovendeerd, T. Delhaas, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux]
Subjects: Sequential estimation, bidomain equations, Observer (quantum physics), estimation, topological gradient, Quantitative Biology::Tissues and Organs, Physics::Medical Physics, observer, Topology, electrophysiology modeling, Term (time), Electrophysiology, Data assimilation, Level set, shape derivative, State (computer science), data assimilation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; We propose a new sequential estimation method for making an electrophysiology model patient-specific, with data in the form of level sets of the electrical potential. Our method incorporates a novel correction term based on topological gradients, in order to track solutions of complex patterns. Our assessments demonstrate the effectiveness of this approach, including in a realistic case of atrial fibrillation.
Published: 2015
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34. Progress Toward using MRI and a Heart Model to Estimate Patient-Specific Indices of Cardiac Function

Author: Dominique Chapelle, Reza Razavi, Jacques Sainte-Marie, Maxime Sermesant, Robert Cimrman, R. Andriantsimiavona, Philippe Moireau, Dlg Hill, and Oscar Camara
Subjects: Computer science, business.industry, Patient specific, Nuclear medicine, business
Abstract: In this article, we present a framework to estimate cardiac function parameters like local myocardium contractility using clinical MRI, a heart model and data assimilation. First, we build a generic anatomical model of the ventricles including muscle fibre orientations and anatomical subdivi- sions. Then, this model is deformed to fit a segmented MRI, using an affine registration method and a local deformable biomechanical model. An electromechanical model of the heart can be simulated on this mesh. Data assimilation makes it possible to estimate local contractility from given displacements. Presented results on simulated data and adjustment to clinical data are very promising. Current work on model calibration and estimation of patient parameters open up possibilities for clinical application of this framework. Resume. Dans cet article, nous presentons un cadre de travail pour estimer certains parametres de la fonction cardiaque (comme la contractilite locale) en utilisant l'IRM, un modele du myocarde et l'assimilation de donnees. Tout d'abord, nous detaillons la construction d'un modele generique du my- ocarde incluant l'orientation des fibres musculaires et les differents segments anatomiques. Ce modele peutdeforme pour s'ajuster aux images cliniques. Un modeleecanique du myocarde est ensuite presentee t simule. Enfin, l'assimilation de donnees permet d'estimer la contractilitel ocalea partir de donnees telles que les deplacements. Les resultats sur l'ajustement du modelea geometrie du patient et l'assimilation sur des donnees simulees sont tres encourageants. Les travaux en cours sur la calibration du modele et l'estimation de parametres du patient ouvrent de nouvelles possibilites pour l'application de ce cadre de travail dans un environnement clinique.
Published: 2005
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35. Simulation numérique du système cardiovasculaire

Author: Jean-Frédéric Gerbeau and Dominique Chapelle
Subjects: Physics, business.industry, Blood circulation, General Medicine, Nuclear medicine, business, General Biochemistry, Genetics and Molecular Biology, Three dimensional model
Abstract: Les progrès réalisés en mathématiques appliquées permettent aujourd’hui d’envisager la simulation sur ordinateur de certains compartiments du système cardiovasculaire. Nous proposons de faire un point sur quelques modèles, en nous focalisant sur la simulation de l’écoulement du sang dans des artères déformables et sur la simulation de la contraction du myocarde sous l’effet de la propagation d’un signal électrique. Nous tentons également de présenter des applications possibles de ce type de travaux., In this article, we aim at giving a non-technical overview of some mathematical models currently used in the numerical simulation of the cardiovascular system. A hierarchy of models for blood flows in large arteries is briefly described as well as an electromechanical model for the heart. We discuss some possible applications of the numerical simulations of such models, for example the optimization of prostheses. We also address the issue of the data assimilation for the calibration of the models.
Published: 2005
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36. Simulation du drapé des tissus par maillages adaptatifs

Author: Houman Borouchaki, Dominique Chapelle, and Julien Villard
Subjects: General Medicine, Humanities, Mathematics
Abstract: Resume La plupart des methodes de simulation numerique du tombe de tissus sont basees sur un modele mecanique s'appuyant, en general, sur un maillage surfacique uniforme. Le tissu etant un materiau tres souple, de nombreux plis peuvent se former sur sa surface lorsque celui-ci est en mouvement libre ou contraint (collisions, points d'arrimage, etc.). Le probleme de la simulation est de faire evoluer le systeme mecanique tout en ayant une representation geometrique realiste de la surface. Il se pose alors un probleme de discretisation adequate de la surface. Pour remedier, a ce probleme, nous proposons une methode basee sur un maillage adaptatif permettant au modele mecanique d'evoluer sans la contrainte d'un maillage uniforme. Nous decrivons aussi un nouveau modele mecanique adapte ainsi que notre methode de raffinement local du maillage. Un exemple numerique vient illustrer l'interet de notre methode. Pour citer cet article : J. Villard et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 561–566.
Published: 2002
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37. Dimensional reductions of a cardiac model for effective validation and calibration

Author: Dominique Chapelle, Matthieu Caruel, Philippe Moireau, Yves Lecarpentier, Radomir Chabiniok, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)
Subjects: Sarcomeres, Beating heart, Engineering, Calibration and validation, Heart Ventricles, 0206 medical engineering, Blood Pressure, Model parameters, 02 engineering and technology, 030204 cardiovascular system & hematology, Ventricular Function, Left, Elastance, cardiac modeling, 03 medical and health sciences, Imaging, Three-Dimensional, 0302 clinical medicine, Afterload, experimental validation, Animals, Computer Simulation, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Simulation, Frank–Starling law of the heart, length-dependence effects, business.industry, Myocardium, Mechanical Engineering, Models, Cardiovascular, Reproducibility of Results, Experimental data, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Heart, Myocardial Contraction, 020601 biomedical engineering, Elasticity, Rats, Preload, Modeling and Simulation, Calibration, Frank-Starling mechanism, hierarchical modeling, Biological system, business, Algorithms, Biotechnology
Abstract: International audience; Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced-dimen\-sional models, in ''0D'' --~typically, to represent a cardiac cavity, or several coupled cavities --~and in ''1D'' --~to model elongated structures such as muscle samples or myocytes. We apply this approach with an earlier-proposed 3D cardiac model designed to capture length-dependence effects in contraction, which we here complement by an additional modeling component devised to represent length-dependent relaxation. We then pre\-sent experimental data produced with rat papillary muscles samples when varying preload and afterload conditions, and we achieve some detailed validations of the 1D model with these data, including for the length-dependence effects that are accurately captured. Finally, when running simulations of the 0D model pre-calibrated with the 1D model parameters, we obtain pressure-volume indicators of the left ventricle in good agreement with some important features of cardiac physiology, including the so-called Frank-Starling mechanism, the End-Systolic Pres\-sure-Volume Relationship (ESPVR), as well as varying elastance properties. This integrated multi-dimensional modeling approach thus sheds new light on the relations between the phenomena observed at different scales and at the local vs. organ levels.
Published: 2014
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38. An inf-sup test for shell finite elements

Author: Klaus-Jürgen Bathe, Alexander Iosilevich, Dominique Chapelle, Massachusetts Institute of Technology (MIT), Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: Shell elements, Discretization, Nuclear Theory, Shell (structure), 02 engineering and technology, Test (biology), Mixed formulations, 01 natural sciences, 0203 mechanical engineering, Data_FILES, Physics::Atomic and Molecular Clusters, General Materials Science, 0101 mathematics, Civil and Structural Engineering, Mathematics, MITC elements, Mechanical Engineering, Mathematical analysis, Mixed finite element method, Finite element method, Computer Science Applications, 010101 applied mathematics, 020303 mechanical engineering & transports, Modeling and Simulation, Inf-sup condition, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We present an inf-sup test for general mixed shell finite element discretizations. The test is useful in the thorough evaluation of a shell finite element discretization scheme. We apply the test to the MITC shell elements and find that these elements pass the test.
Published: 2000
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39. Fundamental considerations for the finite element analysis of shell structures

Author: Dominique Chapelle and Klaus-Jürgen Bathe
Subjects: business.industry, Mechanical Engineering, Nuclear Theory, Mathematical analysis, Shell (structure), Mixed finite element method, Structural engineering, Finite element method, Computer Science Applications, Test case, Rate of convergence, Modeling and Simulation, Physics::Atomic and Molecular Clusters, General Materials Science, Boundary value problem, business, Civil and Structural Engineering, Mathematics
Abstract: The objective in this paper is to present fundamental considerations regarding the finite element analysis of shell structures. First, we review some well-known results regarding the asymptotic behaviour of a shell mathematical model. When the thickness becomes small, the shell behaviour falls into one of two dramatically different categories; namely, the membrane-dominated and bending-dotninated cases. The shell geometry and boundary conditions decide into which category the shell structure falls, and a seemingly small change in these conditions can result into a change of category and hence into a dramatically different shell behaviour. An effective finite element scheme should be applicable to both categories of shell behaviour and the rate of convergence in either case should be optimal and independent of the shell thickness. Such a finite element scheme is difficult to achieve but it is important that existing procedures be analysed and measured with due regard to these considerations. To this end, we present theoretical considerations and we propose appropriate shell analysis test cases for numerical evaluations.
Published: 1998
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40. Direct finite element computation of non-linear modal coupling coefficients for reduced-order shell models

Author: Marina Vidrascu, Dominique Chapelle, Cyril Touzé, Unité de Mécanique (UME), École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Discretization, Computational Mechanics, Shell (structure), Ocean Engineering, Geometry, Bifurcation diagram, Quadratic equation, [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], stiffness evaluation, Mathematics, Coupling, MITC elements, bifurcation diagram, reduced-order models, Applied Mathematics, Mechanical Engineering, Mathematical analysis, geometric nonlinearity, Finite element method, Computational Mathematics, Nonlinear system, Computational Theory and Mathematics, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], finite elements, Reduction (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We propose a direct method for computing modal coupling coefficients - due to geometrically nonlinear effects - for thin shells vibrating at large amplitude and discretized by a finite element (FE) procedure. These coupling coefficients arise when considering a discrete expansion of the unknown displacement onto the eigenmodes of the linear operator. The evolution problem is thus projected onto the eigenmodes basis and expressed as an assembly of oscillators with quadratic and cubic nonlinearities. The nonlinear coupling coefficients are directly derived from the finite element formulation, with specificities pertaining to the shell elements considered, namely, here elements of the ''Mixed Interpolation of Tensorial Components'' family (MITC). Therefore, the computation of coupling coefficients, combined with an adequate selection of the significant eigenmodes, allows the derivation of effective reduced-order models for computing - with a continuation procedure - the stable and unstable vibratory states of any vibrating shell, up to large amplitudes. The procedure is illustrated on a hyperbolic paraboloid panel. Bifurcation diagrams in free and forced vibrations are obtained. Comparisons with direct time simulations of the full FE model are given. Finally, the computed coefficients are used for a maximal reduction based on asymptotic nonlinear normal modes (NNMs), and we find that the most important part of the dynamics can be predicted with a single oscillator equation.
Published: 2014
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41. General coupling of porous flows and hyperelastic formulations -- From thermodynamics principles to energy balance and compatible time schemes

Author: Philippe Moireau, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: thermomechanics, Spacetime, Computer science, Poromechanics, Energy balance, poromechanics, General Physics and Astronomy, Thermodynamics, Laws of thermodynamics, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Isothermal process, biomechanics, Mixture theory, thermodynamics, Classical mechanics, mixtures, Hyperelastic material, hyperelasticity, Porosity, Mathematical Physics
Abstract: Updated version of previously published research report; International audience; We formulate a general poromechanics model -- within the framework of a two-phase mixture theory -- compatible with large strains and without any simplification in the momentum expressions, in particular concerning the fluid flows. The only specific assumptions made are fluid incompressibility and isothermal conditions. Our formulation is based on fundamental physical principles -- namely, essential conservation and thermodynamics laws -- and we thus obtain a Clausius-Duhem inequality which is crucial for devising compatible constitutive laws. We then propose to model the solid behavior based on a generalized hyperelastic free energy potential -- with additional viscous effects -- which allows to represent a wide range of mechanical behaviors. The resulting formulation takes the form of a coupled system similar to a fluid-structure interaction problem written in an Arbitrary Lagrangian-Eulerian formalism, with additional volume-distributed interaction forces. We achieve another important objective by identifying the essential energy balance prevailing in the model, and this paves the way for further works on mathematical analyses, and time and space discretizations of the formulation.; Nous présentons, dans le cadre de la théorie des mélanges, un model poromécanique général valide en grands déplacements et sans simplification sur le bilan de conservation des moments, en particulier pour le système fluide. Les seules hypothèses faites sont l'incompressibilité du fluide et des conditions isothermes. Notre formulation s'appuie sur les principes de la thermodynamiques et nous obtenons une inégalité de Clausius-Duhem fondamentale pour l'obtention de lois de comportement adaptées. Nous proposons alors de modéliser le solide avec un potentiel d'énergie libre hyperélastique généralisé auquel s'ajoute un potentiel visqueux, permettant ainsi de représenter une large gamme de comportements mécaniques. La formulation résultante prend la forme d'un système couplé similaire à ceux rencontrés en interaction fluide-structure de type ALE comprenant un couplage volumique supplémentaire. Nous sommes alors en mesure d'écrire sur le modèle complet des estimations d'énergie qui seront à l'origine de travaux futurs, que ce soit pour l'analyse mathématique du système ou la formulation de discrétisations en temps et en espace adaptées.
Published: 2014
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42. A locking-free approximation of curved rods by straight beam elements

Author: Dominique Chapelle
Subjects: Timoshenko beam theory, Discretization, Optimal estimation, Computer simulation, Applied Mathematics, Numerical analysis, Mathematical analysis, Torsion (mechanics), Geometry, 010103 numerical & computational mathematics, 01 natural sciences, Rod, 010101 applied mathematics, Computational Mathematics, 0101 mathematics, Mathematics
Abstract: We consider an elastic model for a curved rod with arbitrary three-dimensional geometry, incorporating shear and membrane as well as bending and torsion effects. We define an approximation procedure based on a discretization by linear Timoshenko beam elements. Introducing an equivalent mixed problem, we establish optimal error estimates independent of the thickness, thereby proving that shear and membrane locking is avoided. The approximation scheme is tested on specific examples and the numerical results confirm the estimates obtained by theory.
Published: 1997
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43. Dimensional Reduction of Cardiac Models for Effective Validation and Calibration

Author: Radomir Chabiniok, Philippe Moireau, Yves Lecarpentier, Dominique Chapelle, Matthieu Caruel, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, Service d'Explorations Fonctionnelles Cardio-Respiratoires, Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Hôpital de Bicêtre, Ourselin, Sebastien and Rueckert, Daniel and Smith, Nicolas, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: multi scale, 0303 health sciences, Beating heart, Calibration and validation, Hierarchical modeling, Computer science, Calibration (statistics), 0206 medical engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 02 engineering and technology, Experimental validation, heart, 020601 biomedical engineering, Model validation, 03 medical and health sciences, Dimensional reduction, model reduction, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Algorithm, Simulation, 030304 developmental biology
Abstract: To be published as proceedings in: Functional Imaging and Modeling of the Heart 7th International Conference, FIMH 2013, London, UK, Lecture Notes in Computer Science 7945; International audience; Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced- dimensional models, in "0D" - typically, to represent a cardiac cavity, or several coupled cavities - and in "1D" - to model elongated structures such as fibers or myocytes. As illustrations of our approach, we demon- strate model validation based on experiments performed with papillary muscles, and calibration using patient-specific pressure-volume loops.
Published: 2013

44. Surface-based electrophysiology modeling and assessment of physiological simulations in atria

Author: Michel Haïssaguerre, Dominique Chapelle, Jean-Frédéric Gerbeau, Annabelle Collin, Mélèze Hocini, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Hôpital Haut-Lévêque, Université Sciences et Technologies - Bordeaux 1-CHU Bordeaux [Bordeaux], Sébastien Ourselin and Daniel Rueckert and Nicolas Smith, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Sciences et Technologies - Bordeaux 1 (UB)-CHU Bordeaux [Bordeaux]
Subjects: Surface (mathematics), Materials science, Asymptotic analysis, Left atrium, Bidomain model, Cardiology, 3d model, 030204 cardiovascular system & hematology, 01 natural sciences, 010101 applied mathematics, 03 medical and health sciences, Electrophysiology, 0302 clinical medicine, medicine.anatomical_structure, Electrophysiology modelling, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, medicine, 0101 mathematics, Wall thickness, Anisotropy, Biological system, Simulation
Abstract: International audience; The objective of this paper is to assess a previously-proposed surface-based electrophysiology model with detailed atrial simulations. This model - derived and substantiated by mathematical arguments - is specifically designed to address thin structures such as atria, and to take into account strong anisotropy effects related to fiber directions with possibly rapid variations across the wall thickness. The simulation results are in excellent adequacy with previous studies, and confirm the importance of anisotropy effects and variations thereof. Furthermore, this surface-based model provides dramatic computational benefits over 3D models with preserved accuracy.
Published: 2013
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45. Personalization of a Cardiac Electromechanical Model using Reduced Order Unscented Kalman Filtering from Regional Volumes

Author: Alejandro F. Frangi, Stephanie Marchesseau, Nicholas Ayache, Christophe Leclercq, Simon G. Duckett, Karim Lekadir, Reza Razavi, Hervé Delingette, Philippe Moireau, Kawal Rhode, Erwan Donal, Christopher A. Rinaldi, R.M. Figueras i Ventura, Catalina Tobon-Gomez, Dominique Chapelle, Mireille Garreau, Alfredo Hernandez, Maxime Sermesant, Rocio Cabrera-Lozoya, Analysis and Simulation of Biomedical Images (ASCLEPIOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB), Universitat Pompeu Fabra [Barcelona] (UPF), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Laboratoire Traitement du Signal et de l'Image (LTSI), Université de Rennes (UR)-Institut National de la Santé et de la Recherche Médicale (INSERM), Division of Imaging Sciences, King‘s College London, Department of cardiology [Guy's and St. Thomas ' hospitals] [London], Guy's and St Thomas' Hospital [London]-Guy's Hospital [London], NIHR Biomedical Research Centre [London], Guy's and St Thomas' NHS Foundation Trust-King‘s College London, European Project: 291080,EC:FP7:ERC,ERC-2011-ADG_20110209,MEDYMA(2012), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université de Rennes 1 (UR1), and Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de la Santé et de la Recherche Médicale (INSERM)
Subjects: Matching (graph theory), Computer science, Heart Ventricles, 0206 medical engineering, Magnetic Resonance Imaging, Cine, Health Informatics, 02 engineering and technology, Kinematics, Sensitivity and Specificity, Ventricular Function, Left, 030218 nuclear medicine & medical imaging, Reduced order, Personalization, 03 medical and health sciences, Imaging, Three-Dimensional, 0302 clinical medicine, Heart Conduction System, Image Interpretation, Computer-Assisted, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, Humans, Computer Simulation, Radiology, Nuclear Medicine and imaging, Segmentation, Computer vision, Unscented transform, Precision Medicine, Excitation Contraction Coupling, Radiological and Ultrasound Technology, Estimation theory, business.industry, Models, Cardiovascular, Reproducibility of Results, Organ Size, Image Enhancement, Myocardial Contraction, 020601 biomedical engineering, Computer Graphics and Computer-Aided Design, Unscented kalman filtering, Computer Vision and Pattern Recognition, Artificial intelligence, business, Algorithms
Abstract: International audience; Patient-specific cardiac modelling can help in understanding pathophysiology and therapy planning. However it requires to combine functional and anatomical data in order to build accurate models and to personalize the model geometry, kinematics, electrophysiology and mechanics. Personalizing the electromechanical coupling from medical images is a challenging task. We use the Bestel-Clément-Sorine (BCS) electromechanical model of the heart, which provides reasonable accuracy with a reasonable number of parameters (14 for each ventricle) compared to the available clinical data at the organ level. We propose a personalization strategy from cine MRI data in two steps. We first estimate global parameters with an automatic calibration algorithm based on the Unscented Transform which allows to initialize the parameters while matching the volume and pressure curves. In a second step we locally personalize the contractilities of all AHA (American Heart Association) zones of the left ventricle using the Reduced Order Unscented Kalman Filtering on Regional Volumes. This personalization strategy was validated synthetically and tested successfully on eight healthy and three pathological cases.
Published: 2013
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46. State observers of a vascular fluid-structure interaction model through measurements in the solid

Author: Jean-Frédéric Gerbeau, Miguel Angel Fernández, Cristóbal Bertoglio, Dominique Chapelle, Philippe Moireau, Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Modeling, analysis and control in computational structural dynamics (MACS), Inria Saclay - Ile de France, European Project: 224495,ICT,FP7-ICT-2007-2,EUHEART(2008), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Observer (quantum physics), 0206 medical engineering, Computational Mechanics, General Physics and Astronomy, fluid-structure interaction, 02 engineering and technology, hemodynamics, 01 natural sciences, Control theory, Fluid–structure interaction, Fluid dynamics, State observer, Boundary value problem, 0101 mathematics, Added mass, Mathematics, observers, estimation, Mechanical Engineering, Interaction model, 020601 biomedical engineering, Computer Science Applications, 010101 applied mathematics, Mechanics of Materials, Displacement (fluid), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We analyze the performances of two types of Luenberger observers -- namely, the so-called Direct Velocity Feedback and Schur Displacement Feedback procedures, originally devised for elasto-dynamics -- to estimate the state of a fluid-structure interaction model for hemodynamics, when the measurements are assumed to be restricted to displacements or velocities in the solid. We first assess the observers using hemodynamics-inspired test problems with the complete model, including the Navier-Stokes equations in Arbitrary Lagrangian-Eulerian formulation, in particular. Then, in order to obtain more detailed insight we consider several well-chosen simplified models, each of which allowing a thorough analysis -- emphasizing spectral considerations -- while illustrating a major phenomenon of interest for the observer performance, namely, the added mass effect for the structure, the coupling with a lumped-parameter boundary condition model for the fluid flow, and the fluid dynamics effect per se. Whereas improvements can be sought when additional measurements are available in the fluid domain in order to more effectively deal with strong uncertainties in the fluid state, in the present framework this establishes Luenberger observer methods as very attractive strategies -- compared, e.g., to classical variational techniques -- to perform state estimation, and more generally for uncertainty estimation since other observer procedures can be conveniently combined to estimate uncertain parameters.
Published: 2013
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47. A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems -- Analysis, assessments and applications to parameter estimation

Author: Jacques Sainte-Marie, Dominique Chapelle, Philippe Moireau, Asven Gariah, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Modeling, analysis and control in computational structural dynamics (MACS), Inria Paris-Rocquencourt, Numerical Analysis, Geophysics and Ecology (ANGE), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Centre d'Études Techniques Maritimes et Fluviales (CETMEF), Avant création Cerema, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Mathematical optimization, Proper Orthogonal Decomposition, FitzHugh-Nagumo equations, 010103 numerical & computational mathematics, 01 natural sciences, Applied mathematics, 0101 mathematics, Remainder, Galerkin method, Mathematics, Numerical Analysis, Sequential estimation, Estimation theory, Applied Mathematics, Cardiac modeling, Real image, 010101 applied mathematics, Computational Mathematics, Modeling and Simulation, Parameter variations, Proper orthogonal decomposition, A priori and a posteriori, Estimation, Mathematics Subject Classification: 65M60, 35A35, 35B45, 93E10, Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Interpolation
Abstract: We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the FitzHugh − Nagumo 1D model. Finally, we give detailed illustrations of the approach in two parameter estimation applications, the first in a variational estimation framework with the FitzHugh − Nagumo model, and the second with a beating heart mechanical model for which we employ a sequential estimation method to characterize model parameters using real image data in a clinical case.
Published: 2013
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48. A surface-based electrophysiology model relying on asymptotic analysis and motivated by cardiac atria modeling

Author: Annabelle Collin, Dominique Chapelle, Jean-Frédéric Gerbeau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Numerical simulation of biological flows (REO), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria Paris-Rocquencourt, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Subjects: Surface (mathematics), 0303 health sciences, Asymptotic analysis, Mathematical optimization, Computational model, Field (physics), Computer science, Computational electrophysiology, Applied Mathematics, Thin domains, Cardiac modeling, 01 natural sciences, 010101 applied mathematics, 03 medical and health sciences, Modeling and Simulation, Convergence (routing), Statistical physics, Limit (mathematics), 0101 mathematics, AMS Subject Classification: 22E46, 53C35, 57S20, Anisotropy, Representation (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], 030304 developmental biology
Abstract: International audience; Computational electrophysiology is a very active field with tremendous potential in medical applications, albeit leads to highly intensive simulations. We here propose a surface-based electrophysiology formulation, motivated by the modeling of thin structures such as cardiac atria, which greatly reduces the size of the computational models. Moreover, our model is specifically devised to retain the key features associated with the anisotropy in the diffusion effects induced by the fiber architecture, with rapid variations across the thickness which cannot be adequately represented by naive averaging strategies. Our proposed model relies on a detailed asymptotic analysis in which we identify a limit model and establish strong convergence results. We also provide detailed numerical assessments which confirm an excellent accuracy of the surface-based model -- compared with the reference 3D model -- including in the representation of a complex phenomenon, namely, spiral waves.
Published: 2013
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49. Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart

Author: Dominique Chapelle, Philippe Moireau, Vivien Mallet, Marc Fragu, Modeling, analysis and control in computational structural dynamics (MACS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Centre d'Enseignement et de Recherche en Environnement Atmosphérique (CEREA), École des Ponts ParisTech (ENPC)-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Coupling environmental data and simulation models for software integration (Clime), Inria Paris-Rocquencourt, European Project: 224495,ICT,FP7-ICT-2007-2,EUHEART(2008), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris
Subjects: Databases, Factual, Computer science, 0206 medical engineering, Biomedical Engineering, 02 engineering and technology, 01 natural sciences, Personalization, Data assimilation, Software, Software library, Personalized modeling, Humans, 0101 mathematics, Computer Applications, business.industry, Models, Cardiovascular, Human physiology, Modular architecture, 020601 biomedical engineering, Data science, Computer Science Applications, 010101 applied mathematics, Cardiac models, Clinical diagnosis, Model simulation, Database Management Systems, business, Algorithms, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience We present the fundamental principles of data assimilation underlying the Verdandi library, and how they are articulated with the modular architecture of the library. This translates -- in particular -- into the definition of standardized interfaces through which the data assimilation library interoperates with the model simulation software and the so-called observation manager. We also survey various examples of data assimilation applied to the personalization of biophysical models, in particular for cardiac modeling applications within the euHeart European project. This illustrates the power of data assimilation concepts in such novel applications, with tremendous potential in clinical diagnosis assistance.
Published: 2013
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50. Coupling schemes for the FSI forward prediction challenge: Comparative study and validation

Author: Marina Vidrascu, Dominique Chapelle, Mikel Landajuela, and Miguel Angel Fernández
Subjects: Coupling, Mathematical optimization, Applied Mathematics, Numerical analysis, Biomedical Engineering, 010103 numerical & computational mathematics, Elasticity (physics), 01 natural sciences, Stability (probability), 010101 applied mathematics, Computational Theory and Mathematics, Modeling and Simulation, Fluid–structure interaction, Benchmark (computing), Compressibility, Strong coupling, Applied mathematics, 0101 mathematics, Molecular Biology, Software, Mathematics
Abstract: This paper presents a numerical study in which several partitioned solution procedures for incompressible fluid-structure interaction are compared and validated against the results of an experimental FSI benchmark. The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy.
Published: 2016
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